Related papers: Generalized Heisenberg relation and Quantum Harmon…
The Robertson's formulation of the uncertainty relation is the most widely accepted form of the Heisenberg uncertainty relation (HUR). It gets modified when we consider it for entangled particles. But this formulation does not consider the…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…
We test the validity of the Generalized Heisenberg's Uncertainty principle in the presence of strong gravitational fields nearby rotating black holes; Heisenberg's principle is supposed to require additional correction terms when gravity is…
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
The research shows that the Heisenberg principle is the logic results of general relativity principle. If inertia coordinator system is used, the general relativity will logically be derived from the Heisenberg principle. The intrinsic…
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity and black-hole physics. In this scenario, all commutation relations are modified and the…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact…
We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the…
Quantum theory is notoriously counterintuitive, and yet remains entirely self-consistent when applied universally. Here we uncover a new manifestation of its unusual consequences. We demonstrate, theoretically and experimentally (by means…
In this study, we explore the validity of the original Heisenberg position- momentum uncertainty relation for a macroscopic harmonic oscillator interacting with environmental micro particles. Our results show that, in the quasi-classical…
The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant…